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SOCIETYOF PETROIFLIMENGINEERSOF AIME PAPER6200 North CentralExpressway NUMBERDallas,Texas 7’5206

SPE 2388

THIS IS A PREPRINT--- SUBJECTTO CORRECTION

Drilling Performance Optimization and

Identification of Overpressure Formations

By

H. W. R. Wardlaw,The U, of Texas,Austin,Tex.

@ Copyright 1969American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.

ABSTRACT INTRODUCTION

Rock-bitdrillingefficiencyfallsoff at Probablythe most importemtsinglereali-higherrotaryspeedsand at highervaluesof zationin rotarydrillingis that not onlymustweight on bit, due to higherrate of generation rock be fracturedon bottom,but also theof rock cuttingsand the need to expendmechan- fracturedparticlesmust be removedfrom theical energyon their removal. rock face instantlyand efficiently,to provide

for furtherfracturingand drillingprogress.A simplerelationshipis shownto exist

betweendrillingefficiencyand penetration For this purpose,energyis brought fromrate,whethercontrolledby rotaryspeedor by the surfaceto the rock face and appliedasweighton bit. Factorsaffectingeitherof the efficientlyas possible. This energyappearstwo parametersof this relationshipare shown in two forms:to be [I]differentialpressureon bottom,[2]mud characteristics,[3] circulationrate, 1. Mechanicalenergy,appliedthroughthe[4] jet velocity and [5] rock-bitdesign.Ex~ples are citedfrom literature,

rotaryend drill string,and convertedinto itsmost usefulfoz?nthroughthe mechanismof bitconesmd teeth.

Furtheranalysisleadsto an indicationof 2. Hydraulicenergy,appliedthroughpumpwhen to expectdrillingperformanceto depend and drill string conduit,and convertedinto itson impactvalueand when on hydraulichorse-Power. No quite straightforwardmethodsare

most efficientform throughcorrectlypositionedjet nozzles,aimed at the rock face just ahead

explainedfor rapiddeterminationof optimal of the oncomingtooth.economicrotaryspeed,and two for.optimaleconomicbit weight,based on current It has been customaryto considertheperformance. mechanicalenergypurelyas the medium for rock

fracture,and the hydraulicenergyas theThree separatemethodsare offeredfor mediumfor chip removaland bottom scavenging.

identificationof overpressuredformation, Furtherexaminationreveals,however,that theusing only the responseof bit to standarddrillingvariables,thus elhinating the need

processesare by no meansmutuallyexclusive.?n fact,both types of energyplay a part in

to wait for a log to be run or to rely on shale both rock fractureand rock removal. This>determinations. perhapsmore than any otherfeatureof rotary

drilling,has renderedits analysisbyReferencesand illustrationsat end of paper.

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—DRILLINGPERFORMANCEOFTIMIZATIQNAND IDENTIFICATION‘-

68 OF OVIWRESSURE FORMATIONS spE.;:

-.

conventionalengineeringmethodsmore difficult R/N is obviouslynot completelyindependentofthan that of most commonindustrialprocesses. R, it is nearly so. Thus it is not difficult

for us to acceptthe hypothesisof independenceMechanicalSweepout of R/N for conditionsof perfectclesming.

The ordinaryrolling-cutterrock bit In commercialpractice,however,perfectconsistsof three conesmountedon journalsand cleaningdoes not exist. Thus, R/N is notsupportedby ball and rollerbearings. independentof R, but decreasesas R increases

due to increaseof N.The conesare quite free to rotateabout

the Journals. However,becausethe jouf’nals An exsmpleof the relationshipto be ex-are not necessarilyradicallylocated,sad be- pected is given in Fig. 3-A, taken from fieldcausethe axes of generationof the several practice. Eata is for drillingin sandy shalerows of teeth on any one conemay also differ, at about 10,000ft, using 52,500lb on a 1%1/4,the actionof the tooth of a rollingcutter in. bit. l?e~etrationrate at 50 rpm wasrock bit can be quite complex. 17 ft/hour [6.8in./100revs],but at 100 rpm

was 28 ft/hour [5.6in./100revs],and at 150A bit in which the journalshave axes rpm was 36 ft/hour[4.8in./100revs]. ‘llmswe

meetingat the centerof the bit is known as a have a steady,linear-typereductionin penetratrue-rollingbit. Its actionis approximately tion per revolutionac penetrationrate in-cycloidal,and the bit tooth entersand leaves creaseswith increaseof rotary speed. The re-the formationalmostvertically. Many hard- sult is the faniliarfallingoff of responsetoformationbits have approximatelythis action rotaryspeed shown in Fig. 3-B.[Fig.1].

Penetrationper revolution[R/N]fallsFor softerformations,however,the axes off, not only as R increases,but also as R/Q

of the conesare offset,causingat least some increases,where Q is a variablefluid circula-of the teeth to followa trochoidalpath, in tion rate. This is indicatedin Fig. 4, pre-,which some forwardmovementis combinedwith pared from publisheddata on laboratorydrill-the up-and-downaction [Fig.I]. ing of dense limestone,using a 3-7/8-inxdia-

mond bit.hEven with a hard-formationbit, a good

deal of mechanicalaction is used in rock re- A stiilar~esultis obtainedby plottingmoval as well as in rock fracture. It %s variablerate data for a rolling-cutterrockgenerallysupposedthat the rock-bittooth, on bit in field tests.15 The laboratorydata,enteringthe formation,formsa wedge of pul- however,are of particularinterest,as we haveverizedrockmaterialahead of it, which two sets of results,one for 750 psi and onepresseslaterallyon the rock on either side of for zeropressuredifferentialacrossthe cut-the tooth,assistingnot only in fracturing ting zone. The fact that we have a virtuallybut in the rock chip removalprocess. constantvalue of R/N for zeropressurediffer-

ential,providesthe clue to how to obtainConsiderfirsta hypotheticalcase in betterresponseto rotaryspeed:by reducing

which all mechanicalenergyis used in rock pressuredifferentialon bottom.fractureand none in rock cuttingremoval.Under such conditionsit would be reasonableto By increasingcirculationrate,we reducesupposethat drillingspeedwould be directly R/Q and, at very high circulationrates,ap-proportionalto rotaryspeed. Thus, if we preachthe same value of R/N as is obtaineddesignatedrillingspeedby R and rotaryspeed with zero pressuredifferential. Thus a meas-by N, we might expectthe ratioR/N to remain ure of perfect cleaningis achievedby eitherconstantas N increases,or as R increasesas of two alternativemethods.a resultof increaseof N.

Responseto Weight on BitMaurerhas citedan exampleof a test16

under very carefullycontrolledlaboratory Maurerhas shownalso that,with perfectconditions,that were made to approachsuch a cleaning,penetrationrate is proportionaltohypotheticalcondition,describedby him as the bit weight squared. mus, designatingperfect cleaning. The test was conductedon for the bit weight,we shouldexpectR/W2 tohard dolomite[permeabilityzero]with a remainconstantas R increaseswith increasing4-3/4-in.bit, using very low bit weight W, providedperfectcleaningprevails.[4,750lb].

Experimentsconductedby Somerton3,underIf, for this test,we plot penetrationper conditionsin the laboratorycloselyapproaching{

revolution[R/N]vs penetrationrate [R],we perfectcleaning,obtainedjust such a result.obtainthe graph shown,in Fig. 2. Although Fig. 5, using Sornerton’sdata> shows that for

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*

SPE-2388 H. W. R. WARDLAW 6

his experimentsR/W2 remainedvirtuallyinde- [Fig.8-B].9’10pendentof R as R was increasedby increasingw. A possibleexplanationis that perfect

cleaningrefersto a conditionwhere,not onlyIn practiceR/W2, insteadof remaining are the rock chipscompletelyscavenged,but

constant,decreaseslinearlywith R, as R the solidscontainedin the drillingfluidincreaseswith increasingW. This is illus- also.tratedin Fig. 6, using data for drillinginpermeablelimestoneusing a L1/8-in.-diameter DifferentialPressurerock bit.k Similarresultsare obtainedformost sets of data whereW is the independent It is generallyacceptedthat an increasevariable. in pressureacrossthe bottom of the hole

causesa decreasein drillingrete.UnperfectCleaning

Intuitively,we might seek a hyperbolicThe objectof the R/N vs R plot, aad the relationshipbetweenpressureP and drilling

R/W2VSR @Ot,with increasingN and W, re- rate R, where the productR x P would remainspectively,is to formalizethe relationships constant.of rate-weight-speed[R-w-N]for imperfectcleming sad to providea comparisonwith Such a relationshipdoes not fit the data.perfectcleaningconditions. However,if R x P is plottedagainstR, a

linearrelationshipis foundto existwhich isMaurerhas suggestedan alternative quiteusefulin predictingresultsof pressure

formalization,using exponentsinsteadof co- changes.efficient, and citesnine otherauthoritieswho have suggestedformalizedrelationships Cunninghamhas made some classicexperi-using exponents. There is considerablelack of ments on sandstone,using a microbitwith aagreement,however,on the valuesto be wide variationof pressuredifferentialsre-assignedto these exponents. Moreover,the ex- tweenboreholeand pore pressures.13ponentialformulasdo not lend themselvesreadilyto rig-floorcalculation,which is a If, for this data, R x P is plottedvsseriousdisadvantage. R, a seriesof straightlines resultssimilar

to that shownin Fig. 9.Furthermore,a linearrelationshipsimpli-

fies graphicalcomparisonsand can lead to some Such a linearplot is usefulin that itusefulnumericalcomputations. enablesinterpolationof data for pressure

valuesotherthan thoseexistingduringtheIf, however,we are to compareimperfect test, as shownin Fig. 10. Any givenpressure

cleaningwith perfectcleaningconditions,we P allowsus to fix the relationshipR x P tomust be reasonablysure of what constitutes R passingthroughthe origin,and the intersec-perfectcleaning. tion of this with the line representingthe

test data will give the requiredinformation.For example,the point of zeropenetration

rate and maximumR/W2 indicatedby the arrow in Fig. 11 showsthat the relationshipisFig. 6 m&ht conceivablybe thoughtof as sensitiveto changesin Jet velocity[V].perfectcleaning,sinceat that point there are Furthermore,extrapolationto both verticalandno rock chipsto be removed. horizontalaxes is of specialinterest. !lTnis

is shown in Fig. 12.Some supportfor this view might arise

also from the fact that plote of R/W2 vs R for The pointsA,B,C representingthe penetra-two conditionsof pressuredifferentialon tion rates for zero differentialmay be readilybottom convergeon such a point,as indicated plottedvs jet velocity,as shownby the linearat point C on Fig. 7, using data publishedin relationshipin Fig. 12-A.the literature.7

Conversely,the points D,E,FrepresentingIf, however$we compareplots in which R x P at high valuesof P are linearlyrelated,

the d illingfluid is changedfrom mud to6

not to V, but to V2, as shown in Fig. 12-B.water , we find that the linesdo not convergeto such a point. Quiteevidently,PointsA and These valuesare, of course,extremeval-B of Fig. 8 are far from coincidental. ues. Most resultsfrompracticelie somewhere

betweenthesevalues>approachinglow pressureDifferencesoccuralsowhen comparingsets [A,B,C]for surfaceformation,and high press-

with differentjettingeffect [Fig.8-A] or ure [D,E,F]for tight formationsat depth.with differentratesof circulation

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DRILLINGPERFOWCE OPTIMIZATIONAND IDENTIFICATION-1 OF OVERPRESSUREFORMATIONS SPE-2M

~ TIE demonstrationmay also interestthosewho, in the past, have advocatedeither “im-pact value”

4Qx V] or jet hydraulichorse-

power [Qx ] for variousdown-holeconditions

IEtectionof High FormationPressures

IIIdrillingcetiainformations}notablyinthe Louisiana-TexasGulf Coast=d in deepzones in West Texas,it is customaryto en-counterformationshavinga pore pressuredif-feringappreciablyfrom the normalhydrostaticgradient. Among these fomations, the perme-able sectionsare identifiablein causingakick or flow tendency,often requiringincreasein mud density. However,the high pressuresare not confinedto the permeablezones,butare commo~also to the adjacenttight forma-tions, such as shales. These latterdo notgive rise to kicks,but neverthelessoften givetroubleunlesspropermud densityis used.

As mud densityis increasedbeyondthatnecessaryto balanceformationpore preesures,backpressureon the formationcausesthe dxill-ing rate to decrease. Converselyan increasein pore pressuregradientfor a givenmudweightwill causedrillingrate to increasedutto reducedbackpressure. Furthermore,opera-tion at boreholepressureappreciablybelowpore pressureis hazardousand may lead tocollapseof hole wall in low strengthformatiolsuch as shales.

It is important,therefore,to be able toestimatethe overbalanceexistingon bottomand to recognizechangesin this overbalancebefore it is too late.

The relationshipestablishedfor R x P vsR is usefulfor this purpose.

Algebraically,the relationshipmay be ex-pressedin the form:R x P ~ a - bR, wherea and b are constantsfor the fomation anddrillingconditionsbeing used.

From this we obtainP ~ [a/R]-b, [a/R]‘b + P, [1/R]= [b/a]t [1/a]P.

In otherwords drillingtime [inminutesper foot, for exsnple]is linearlyrelatedtopressuredifferential.

Fig. 13 showsthe relationship,using dat[from the previousexample.~ ComparisonofPointsA and B indicatesthat reductionofoverbalancefrom 110 lb/galto 0.2 lb/galmighlreducedrillingthe from 4.3 min/ftto about2.8min/ft - a significantreduction. Thisfact is used in practiceto identifythreatene(blowoutsby the so-calleddrillingbreak.

The linearrelationshipshown in the fig-

ure in fact suggestsa methodwherebythe lossof’overbalancemight be predicted“quantitative,ly” if drillingtime couldbe establishedforseveralmud densitieswhile othervariablesarekept reasonablyconstant.

. Effectof Weight and Rotary Speedon High-PressureIdentification

If high pressureis encounteredfollowinga changeof rpm or bit weight,identificationis stillpossible,providedcertainprecautionsare taken.

Fig. 14 showsa plot of R/W2 vs R that hasbeen establishedfor a normallypressuredformation. Responseto say intermediatebitweight shouldfall on the straightline thusestablished. However,if responsefallsout-side this line,as at PointA, the fozmationis p~obablyoverpressured,even thoughtheremay be a tendencyfor flow,due to low forma-tion permeability.

Fig. 15 showshow overpressuremay beidentifiedin the case of a previouslyestab-lishedrelationshipfor variousrpm. Point B,for exmple, is clearlyoutsidethe trendestablishedfor normalpressuresat a givenbitweight.

Methodof optimizingRotary Speed

The relationshipsestablishedmay be usedfor optimizingrotary speedor bit weight,forminimumcostper foot.

For rotaryspeed,we use the R/Nvs Rrelationshipas indicatedin Fig. 16. Now pro-ceed as follows:

1. Extrapolatethe line to verticalandhorizontalaxes}PointsA and B.

Dividevalue at point B[53]by valueE$ po~~ ::38/100] givinga value [1OOx 53]/

= , Designatethis valueas “keyrpm”.

3. Multiply“keyrpm” by the ratio of bitlife to round-triptime. Example:“keyrpm”~ 140;bit life ~ 10 hours;round-triptime ~6 hours;near optimumrpm = [1~0x 101/6 ~ 234rpm.

Such rpm may then be tried for a while,and eventuallycheckedagain for optimum,asbefore.

Justificationof thismethod is given inAppendixA.

OptimumWeight on Bit

Optimizationfor bit weight is similarly

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●

SPE-2388 H. W. R. WARDGAW 71

obtained,as shownin Fig. 17. 10● Binghm, Mo G.: “FieldResultsSupportLaboratoryConclusionson Transport-Limit

Procedureis as follows: Drilling”,Oil and Gas J. [March1, 1965],u. Cunningham,R. A. and Eenink,J. G.:

1. Extrapolatethe line to the vertical “LaboratoryStudyof Overburden,and horizontalaxes, PointsC and D. Formationand Mud ColumuPressureson

DrillingRate of PermeableFormations”,2. Dividethe value at PointD [63]by

the value at Point C [&3/1,000],givinga-eTras., MME [1959]&&t~d~70f Energy

12. Wardlaw,H. W. R.:value of 1,465. Designatethis valueas “key UtilizationDuringRotaryDrilling”,W-squared”. Multiply“keyW-squared” by the PhD Dissertation)The U. of Tex. Austin,ratioof bit life to round-triptime. Exemple: in progress.Key W-squared❑ 1,465 [1,000lb squared];bit 13. Cunningham,R. A.: “LaboratoryStudieslife = 16 hours;round-triptime = 8 hours; of Effectof RotarySpeedon Rock Bitnear optimumbit weigkt in thousandsof pounds Perfozm%nceand DrillingCost”,Drill.ant‘{[1,465 x 16]8=== 54; near-optimum 14 mod. Wac., 01 [1960]7.bit weight = 5h,0001b. . Galle,E. M. and Woods,H. B.: “Best

ConstantWeight and RotarySpeed for

Justificationof this method is given inRotaryRock Bits”)Drill.and Prod. Prac.~

AppendixB.API [1963]48.

15● Moore,PrestonL.: “FiveFactorsthat

Bit Weight/Affect DrillingRate”,Oil and Gas J.

rpm Combination16 [Oct.6, 1958].

The bit weightthat is right for one level. Rowley,D. S., Howe, R. J. and Deily,

F. H.: “LaboratoryDrillingPerformanceof rpm may be wrong for a different~m; there-fore an rpm checkshouldbe carriedout as soon

of the Full ScaleRock Bit”, J. pet. Tech.[Ju., 19611 71-81.

as opttiumbit weightis established. If nec-essary,a furtherbit-weightand rpm check APPENDIxA --shouldbe made until conditionsstartto show a

DERIVATIONOF FORMUIAFORBEST ROTARYSPEED

stabilizedoptimum.

Definitionof TermsREFERENCES

c= drillingcost,dollarsper foot drilled1. Maurer,W. C.: “The ‘PerfectCleaning’ = rate of penetration,ft/min

Theoryof RotaryDrilling”,J. Pet. Tech.~ [Nov., 1962] 1270-1274.

R/6: = rate of penetration,ft/hourN= rotaryspeed,rpm

. Wardlaw,H. W. R: “SimplifiedAnalysls n= total revs of bit beforepullingAids in OpttiizingDrillingFactorsfor t x numberof minutesdrillingbeforeMinimumCost”,J. Pet. Tech. [May,1961]475-482.

pullingbitm = time taken for roundtrip,minutes

3. Somerton,WilburH.: “AIaboratoryStudy m/60 ❑ time taken for roundtrip,hoursof Rock Breakageby RotaryDrilling”, s = slopeof’performancechart [R/Nvs R]Trans.,AIME [1959] a= verticalinterceptof performancechart

4. van Lingen,N. H.: k= rig cost,dollars/hourA Major FactorGoverningPenetrationRatesat Depth”,J. Pet. Tech. [Sept.,1959] Hours drilled = & = &232-239.

60N

5. Eckel,JohnR.: “Effectof Pressureon.RockDrillability”,!llrans.,AIME [1958] Hours (drilling+ round-trip) = &N + ~213, 1-6.

6. ~ghm, M. G.: “Full-ScaleTests ShowEffectsof Hydraulicson IowerDrilling

[

~&+m-Limit”)Otl and Gas J. [Aprils, 1965]. ‘(30 N -

7. BWhsmI, M. G.: “HowChangesin Rock andPressureAffectthe TransportUnits”,Oil and Gas J. [Feb.22, 19651.

[Cost (drilling + round-trip) = ~ # + m

8. B@@ui, M. G.: “HowLCWI?~)lri~ingL&nitAppearsin LaboratoryDrilling”,Oil andGas J. [I&rch22, 1965].

Footage drilled = ~

9. mm, M. G.: “MultiplePerformanceLine Is SpecialCasebut Can Be Used”, But zl=a-~~Oil and Gas J. [MC.7, 19641. N

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DRILLINGPERFORMANCE0FT1241ZATIQNAND IDENTIFICATION72 oF’C)VERF%’ESSUREFORMATIONS SPE-2388

1aN— -sN

‘R

N ~[1

l+sN .X=an

So that:

Cost/ftdrilled

c =* [-+nj~+srj

[= 60an N 1+msN+sn+m+i%=iiii’md

= O for minimum cost/ft.

So that:

N2 ‘L’opt ms

~

Butn=Nt*

NtSo that N2 = —

opt rns

N

()

N t=—and—,

opt N msopt

Sincet, m and s are known,

()Nas —N

approaches 1opt

Nt

approaches — ●

opt ms

APPENDIXB -- DERIVATIONOF FORMULA‘FORBESTWEIGHT ON BIT

Definitionof Terms

C = drillingcost,dollars/ftdrilledR= rate of penetration,ft/minute

R/60 G rate of penetration,f’t/hourN = rotaryspeed,rpm

Bearinglife in to&l revolutionsis inde-pendentof rotaryspeed.13

n = total revs of bit beforepullingt= number of minutesdrillingbefore

pullingbitm= time taken for roundtrip,minutes

m/60 = time taken for roundtrip, hoursw= weight on bit, thousandlbW2 = weight on bit times itself

Wept = optimumweight on bit [forlowestcost]

s= slopeof perfozmancechart [R/W2 V6 R]b= verticalinterceptof performancechartq = bit life coefficient= nW2k = rig cost, dollars/hour

Hoursdrilled= & = ~ = &WZ60N

Hours (drilling+ round-trip)= * + ~

RnFootagedrilled= ~ =

$*

But ~W2 =b-SR

1 ..&R

- SW2

So that:

Cost/ft drilled

c= *[* +Xljpsd]

kN

[--+‘Kmv @+ms 1+qS+m

TdC

[

-$ 1kN

x= + 2msw G

= O for minimum cost/ft.

So that

-.&__ = mSWopt

opt

W’opt ~ == n)NS~

But q = n~’.

So that W4nW2

opt ‘=

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)%?%38 H. W. R. WARIXAW 73

Sincet, m and S are known,

()was —w approaches 1opt

w’ approaches $opt

For higherbit weights,bit life is inverselyproportionalto weighton bit squared[seeRef.14 and tablebelow].

Weight/in. G— -L [F]*IX1O-65,000 lb 1650 2.506,OOOlb :; 1195 2.647,000lb 55 884 2.678,000lb 63 665 2.649,000lb 71 502 2.54

Im?lmmx c -- DRILLINGTIME TESTS

Drillershave long been awarethat theratea bit drillsis a good indicationof itscondi~ion,i.e., sharpor dull,the type offormationbeing drilled,or whetherthe factorsof weight,rotaryrpm, and hydrauliceffortwere beingproperlyemployed. A sharpbj%zused in the kind of formationfor whi’~ i --asdesignedand properlyrun, will drill 1. .erthan a worn bit used in the wrong kind oz rocksor run improperly. To this extentthe drillerwill observeperiodicallyhow much the isneededto drill a foot,10 ft, or the kellydown. This time will be converted--usuallymentally--intofeetper hour, the usualbasisfor comparingbit performance. Many rigs areequippedwith drillingrate recordersthatenablequickreviewand comparisonof ratesofpenetrationbeing obtained. If automaticdevicesare not available,the drillerwillcheckthe time requiredto drilla foot or moreby markingthe kelly,takinginto accountthatweightslackedoff is the same at the end ofthe test as was put on the bit when the testwas started. The time inrninutes[or seconds]to make a foot,or longerinterval,is notedfor comparisonwith drillingtime testsmadeearlieror later. Thismanner of timingtherate of penetrationis easilyunderstoodand isthe most commonway of judgingperformance. Itwill usuallysufficefor rough estimates of bitperfommnce, but is subjectto errorsthat csabe misleading.

A more exactmanner of measuringrate ofpenetrationis the drill-offtechnique origih-ally suggestedby ArthurLubinski[1956]. This

methodmakes use of’ the fact that the drillstringis an elasticmedium--justas a spring--whose lengthvarieswith its tension, Themethod is employedby slackingoff a givenamountof weighton the bit .md tying down thebrake. Circulationand rotaryspeeda!remain-tainedat constantrates. The bit is allowedto drill off some of the appliedweight;i.ec,more weight of the drill stringis suspendedfrom the crownblock,thus less weight isimposedon the bit. Carefulobservationof thetime neededto drill oft a gZven amountofweight is taken,usuallyin incrementsOr2,000tcl 5,000 ltJ..Time determinationscan best beobtainedusing a stopwatch,particularlyforfast drillingrates,notingthe numberofsecondsrequiredto drilloff the weight incre-ment. Weight-on-bitwill changewith eachdrill-offtest unlessadditionalweight isslackedoff. Drillingtests to determinethebest weight can be ~btainedquicklyby drill-of~runs as shownby the followingtable. It iSimportantto repeatthe processseveral.timesto obtaingood average values despitethe effeclof small changesof formationcharacteristics.

DRILL-OFFTESTS IN SANDY SHALE

Bit Weight [1,000lb] Secondsto Drill Off

70- 65 2665 - 60 2660- 55 25 [Bestw]55- 50 2850-45 3145 - 40 3440- 35 3635 “ 30 5230-25 70

..Hole size was 9-5/8 in., depth10,36oft, drillcollars 63o ft, 5-tn.-ODdrillpipe 9,730 ft,rotaryrpm 130 to 135, and bit hydraulicpower,434 Hhp● Thesetests showedthe best run was25 seconds,obtainedusingweight-on-bitofabout 60)000lb.

Drill-offtests can be convertedfromsecondsto drill o~f a given szoountof weight bmaking a pick-up~d slack-offchart,per Figs.1 through4. This chart,based on the condi-tions of the examplegivenabove,showsthat0.06-ftkellymovementis obtainedfor each1,000-lbweightdrilledoff’.This can be con-vertedas followsimto feetper hour rate ofpenetration,using the best run of 25 secondsto drill off 5,000 lb as shownin the table.

Drillingrate [rt/hour]=

3,6ooX 0.06xWt. DrilledOff [1,000lb]Secondsto DrillOff

= 3,600x~

= k3ft/hour. 4

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Drill-offtests cm be used to determine of energy [interms of bit rotationsper footthe best rotary speedby varyingrpm while drilledat a given loading]requiredfor theholdingconstantthe weight on bit and hydraulic fracturingprocess [assumingperfectcleaningeffort. Stiilarly,the effectof increased of the hole bottom,or no mechanicalenergyhydraulicpower at the bit can be measuredby requiredfor scavenging].varyingthat factorwhile holdingbit weightaadrotary speed constant. The secondterm [(b/a)N] may be regarded

as the mechanicalenergy [interms of bitAPPENDIXD -- -EXPLANATIONOF LINEAR rotationsper foot drilledat a given loading]PERFORMANCERELATIONSHIP requiredfor the scavengingor removalprocess.

It is swell known principleof fluidThroughoutthe latterpart of the test of dynsmicsthat the stressrequiredfor movement

this paper examplesare givenwherebyperform- of liquidis proportionalto the strainrate ofante data from laboratoryor field checksyield the liquidmovement. Sincethe strainrate ofa linearrelationshipof the form: the rock-fragmentslurrywill be in proportion

[1] ~=a.to the rotary speed,such a relationshipcan be

bR [forrotaryspeed changes] readilyunderstood.

or [2]$=c- dR [forbit weight changes]. A rigorousproof of the relationshipindi-

Takingthe firstof these relationships,catedwill not be presentedhere$ and consider-able expertientationmay well be requiredbefore

we have: such formalpresentationcan be made.~N=

a-bR Relationshipfor PressureDifferentials

~ .~ -bNR An empiricalrelationshipfoundto apply

for the effectof pressuredifferentialhas the1 = ‘R~ - bN form:

aN =l+bN (4)Rx P=e-fR.-X-

From this,we obtain:N1

“N . . . . . . . . . . . [3]T=T+a P=*-f

Eq. 3 now statesin algebraicform that the enumberof bit revolutionsrequiredto drill a —=f+p

Rgiven mount [footage]of hole can be repre-sentedby a fixedvalue [l/a]plus a multiple

+= (:) + (:)P.of the rotary speed [(b/a)N].

The fixed value [l/a!,being independent In otherwords, drillingtime [inminutesof rotary speedmay be regardedas the amount per foot, for exsrnple]is linearlyrelatedto

pressuredifferential.

.~b%

>-

- ,2P.

A

ACT!ON OF”TRUE ROLLING” BIT “OFFSET” BIT DESIGN ACTION OF BIT WITH “OFFSET” DESIGN

Fig. 1 - Mechanical sweep-out.

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r ft/fev x 10’

“pERFECT CLEANING” RELATIONSHIP3

I

Ref. 16

rpm 60.180 240 ioo

RPM Increases @

o 2 4 6 ft I hour

Penetration Rate(R)

16F%g. 2 - “Perfectcleaning”relationship.

ITinches/ K)Orevolutions

10

s

s

EFFECT OF ROTARY SPEED

Ref. 2

\ 50rpmo

“\ K)Oromo

\

150 rpmo%

Rotary Speed kew

I *

‘“Penetrototion fb%[R)-ft/hr~$0

I

~lnchss/revolution x 10’20

~

15

10

c

(

EFFECT OF CIRCULATION RATERef. 4

5amovalueo 3

0 ‘0 c1 Zero DifferentialAcross Bottom

\Pressure Dlffsrontlal

=750psiAwoss Bottom

@Clrcubtlan Rate Increases

20 40 60indros/gallonx IOJ %

4Fig. 4 - Effectof circulationrate.

- ft./hr.

i

40

30

2(

u

v 40 100

Rev&on8 per minute ~150

2

Fig. 3-A Effectof rotaryspeed. Fig. 3-B

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%.

~R’w’“’’”’’v”’

q

!——–--—--- --–---—-r J___

i

I ?:....... .. .. .. -.’ . . . . 5 . . . . .. W+W1O....

;.t ~-.- —__ . . . ..__r

!!!& .—=6

. . . . .. . . ..,$ . . . -- -.. .-. .. CW.*> . . . .?

r<“’”’’0”’,.,\

‘\ 0

so \R/Wa

10

\

0

0

!9

m wd@lcrwW3\

!0Penolraflo# Raft (R) - cmjkln -D

Penetration Rate (R) - relotlve-

Fig. 5 - “Perfect cleaning” Fig. 6 - Effect of bit weight.4

+-=’R’W’’”o”m

I

Penetration

Fig. 7 -

Rots (R)- ft/tw+

Effect of bit weight

relationship.3

‘ ,#.,.......-.......,.

z . . .

‘ ‘. rnd-.

I sit Wqht IIMWO1*S

e

I (,0 Zo so

Penetration Rete[R)-ftlhre

Fig. 8-A - Effect of bit weight8

and mud type.

o

‘0, o

.

6. ml.wnrcnm,,

.,. .

?m9twtlen R,v, m. II/w

Fig, 8-8 - Effect of bit weight9

and jetting effect,

and back pressure.7

r cdl . d

t

k‘y

W WMllmwln

‘i.

P*84,t,*&Reto(n1 -lA-

Fig. 8-C - Effect of bit weight10

and circulation rate.

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.

LRnP[xl&)

,6

.

m

Pressure0. Increases

o!0

penetration R% (R)- ft/hr=

Fig. 9 - Effect of pressure I,11

Fig. 12-A - Effect of11

jet velocity,

r RIP(XIOII

I

‘\.\

‘‘/!3 *.

- *U/

1

#m..t’ ,IKO.

Pressure #m, ,Sw

Increosos ,’ ,,00

L..e- ,400

b #* ,$00

●,.

.,&’ C’;m

\

,00“B

/

o“ 10 20 A-” w

40.

M 0

?0

E. .

u

‘uv.215ftA+c

!0 . . .

.,. . .

0

0 ,0

Penetrollon Rate (R). ft/hr _

Fig. I(I - Effect of pressure Il.11

r“”-’”’.,

~f

,. I

‘Fig, 12-B - Effect of11

jet velocity.

Fig. 11 - Effect of pressureand jet velocity,

Led-rmswrc ?it”lo,mo)Pd

Fig. 13 - Drilling time vs11

overbalance.

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F(R/d)

20. ~ ~

10--

L

a-

Sit Weight Increoses

*

0 10 20 d to

pen~trotion Rate (R) - ftihr ~

Fig. 14 - Effect of well pressure.2

+/N)x100

-,

F (MOX too

I40

.

30

~;\

RPM

)0

s100 0 120r*ml

Wft/w

Zo

!00

z00

10R. PM. increase

*

o 20 46 m

Penetration Rate (R)- ft/hr ~

Fig, 15 - Effect of well pressure.2

40 .

30 .

20 -

10.

D#

2U

Pcns?ra~on Rats (R)-*Oft/hr_

Fig. 16 - Optimum rotary speed.2

Fig. 17 - Optimum weight on bit.7

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